COSMIC RAY ANISOTROPY I N INTERPLANETARY SPACE"

SUBWTTeb FOR THE AWARD EC Of

Under the Supervision of

DR. BADRUD0IN

DEPARTMENT OF PHYSICS ALI6ARH MUSLIM UNIVERSITY

ALIGARH ( INDIA)

June, 2005

'p^^^-"G *f!sri

^'T FB^ «^«^

969esa

Dr. Badruddin Reader

Department of Physics Aligarh Muslim University, Aligarh-202002

Phone:0571-2701001(O) :0571-2720162(R)

Fax : 0571-2700093 : 0571-2701001

e-mail: badr phvsfgivahoo.co.in

Dated: /7/V-'^'^^'

CERTIFICATE

I certify that the M. Phil, dissertation titled "Cosmic ray

anisotropy in interplanetary space" is based on the original

research work carried out by Mr. Munendra Singh under my

supervision.

Supervisor

(Dr. Badruddin)

Acknowledgement

I express my sincere gratitude to my supervisor, Dr. Badruddin, for providing his able guidance, kind support and blessings: all the ingredients necessary for this work.

I am grateful to Indian Space Research Organization (I.S.R.O.) for providing all the necessary monetary help through their RESPOND program.

I also want to thank all of my fr iends/ colleagues who helped me directly or indirectly \r\ the accomplishment of this work. May god help them.

-Munendra Singh (ss2008mm@yahoo.co.uk)

Contents

1. The cosmic radiation^ Reviewing the present and future 01

1.1 Cosmic rays within the atmosphere 01

1.2 The elemental composition 02

1.3 Energies and intensities 04

1.4 The stable and radioactive isotopes 05

1.5 The highest energy cosmic rays 05

1.6 Cosmic rays in interplanetary space 06

1.6.1 Short term cosmic ray intensity decreases 06 1.6.2 Long term variations 07 1.6.3 Daily variations 07

2. The interplanetary medium 09

2.1 Solar wind and interplanetary magnetic field 09

2.2 Impacts of solar and interplanetary phenomena at the E a r t h 11

2.3 Magnetic domain of the interplanetary space- The Heliosphere 15

2.3.1 Size of Heliosphere 17 2.3.2 Hehospheric neutral sheet 18

3. Solar modulation of galactic cosmic rays 21

3.1 Solar modulation: Basic processes 21

3.1.1 Diffusion 21 3.1.2 Effects due to the large scale magnetic field 22 3.1.3 Convection 23 3.1.4 Energy change 23

3.2 Solar modulation^ Theoretical models 23

3.2.1 Predictions of models 26

4. Anisotropic cosmic ray modulation 28

4.1 Diurnal anisotropy: basic concepts and its importance 28

4.2 Harmonic analysis 33

4.3 Data analysis 34

4.4 Results 35

4.5 Discussion 60

4.6 Conclusions 60

References 62

CHAPTER - 1

The cosmic radiation: Reviewing the present and future

CHAPTER-1

THE COSMIC RADIATION: REVIEWING THE PRESENT AND FUTURE

Victor Hess discovered a penetrating extraterrestrial radiation in

1911, later called cosmic rays. The search for the origin of cosmic rays

gave birth to many new scientific disciplines, each evolving into a life of

its own. Examples include the discoveries of new elementary particles,

high-energy physics, radioactive particle dating, dating geological

formations and establishing the age of galactic cosmic rays. Cosmic ray

research has become an important part of astrophysics, especially

gamma ray and radio astrophysics.

Starting with balloons and then aircrafts, cosmic ray study has

come into the era of satellites. Scientists design and build instruments to

be carried by satellites and deep space probes - now the magnetospheres

of planets and the heliosphere has become the laboratory in space.

Through experiment and theory we now have a remarkable, but terribly

incomplete, understanding of the origins and physical mechanisms of the

cosmic rays. A brief discussion of cosmic rays and related facts is

discussed below (for more details, see Dorman, 2004).

1.1 Cosmic rays within the atmosphere

Atmospheric gases are a target for the arriving primary cosmic ray

nuclei. Figure 1.1 shows this interaction and the resulting products

(divided in three groups: electromagnetic, hard and nucleonic

components). The external geomagnetic field determines the latitude of

access to the atmosphere by the charged cosmic ray nuclei. For example,

only the cosmic ray nuclei with energies > 12 GeV per nucleon enter at

the geomagnetic equator, whereas all but the lowest energy nuclei have

access over the polar regions and produce a nucleonic cascade that can be

detected by neutron monitors. Thus, the latitude effect was used both to

prove that the cosmic rays were mostly positively charged particles and

to show they had a broad energy distribution.

Incident Primary Particle

Low energy rsucleonic component (disintegration product neutrons

•^degenerate to "slow" neutrons)

Electromagnetic or "soft" corriponenf

Meson or "hard" component

Energy feeds across from nuclear to electromognetic interociions

Nucleonic component N,P=High energy nucleons

n,p = Disintegration 1 Product

. 1 - . - . . •—m-

1 Small energy feedback nucieons 1 from meson to nucteonic Jt>. = Nuclear 1 tO'^Ponent disintegrotion

Fig. l.i: Schematic of secondary radiation production. Ionization chambers mainly monitor the meson and soft component, whereas neutron monitors measure exclusively the nucleonic component.

1.2 The elemental composition

The cosmic rays contain all the nuclei, from Hydrogen to

Uranium. During their acceleration and propagation in the interstellar

medium of our galaxy, these elements have been totally stripped of all

their electrons so that they arrive in the solar system as the bare nuclei.

The cosmic rays represent the only contemporary sample of the elements

from the galaxy that is directly accessible to the observer in the solar

system. Clearly, the cosmic rays are nuclear messengers from the galaxy

with unique information on their nuclear origin.

In Figure 1.2 the relative abundances of nuclei in the cosmic rays

are compared with abundances of elements in the solar system.

- a

DC

10

hHe

iO

S' ! * r-II ^ ? S

Fe

CaTi Cr

1 Na

\ F

II ?/ ' -11 V i ( . , 1

P,?, ClK

f-i w -,Mnj,' -

' Co H

10

1 • w

r Sc

• Satellite

o Solar system

Be i l l I I I I I ! i I l,J,..l, I .1, 1 1.,.1,-L.

0 4 8 12 16 20 24 28 Nuclear Chorge Number

Fig. 1.2: Elemental composition from hydrogen to Nickel in the cosmic rays arriving near the top of Earth's atmosphere. The solar system relative abundances are shown normalized to the cosmic ray Carbon abundances.

The overall similarity between them is apparent with two

exceptions"- Lithium (Li), Beryllium (Be) and Boron (B) and e lements

from Chlorine (CI) to Manganese (Mn). The anomalously high

abundance of these elements is due to the fact tha t as the abundant high

energy Carbon, Oxygen and Iron nuclei propagate through, and collide

with, the gas atoms in the interstellar medium, they knock off fragments

at high energy (such as Li, Be, B) which then become a secondary

addition to the radiation measured by the investigator. These secondary

carry critical information concerning the accelerated cosmic ray nuclei

tha t are propagating through the interstel lar mat te r and magnetic fields

(see Figure 1.3).

o

o o

O

CC

o w —

o

i / i OJ

3 O

CO

ProDaaotion via aolactic disk -Energy loss by ionization -Spoliation. . -Escape . -Rodioactive decoy

Accelej;ation! OaloOic propagation in -*n infersiellor magnetic fields

-*-i

Solar modulation in interplonetary magnetic fields

Fig. I.3: Sketch of the hfe history of an accelerated cosmic ray nucleon.

1.3 Energies and intensities

Figure 1.4 shows a generic energy spectrum of cosmic rays.

2pro}ons per square centimeter per second

a few protons per square kifometer per century.

™C 108 iQio iot210^4 iQie jQie jo2o

Energy (electron volts)

Fig. 1.4: The approximate energy-intensity spectrum of cosmic ray protons in the solar system.

Over 99% of the nuclei are in the energy regions "A" and

measured by spacecraft and balloon instrumentation. For energies in the

region "B", space shuttle sized instruments are essential. Beyond the

energy range "B" the nuclei are probably of extragalactic origin. At the

highest energies (region "C") huge, ground based detector arrays are

required (Simpson, 1997).

1.4 The stable and radioactive isotopes

The isotropic composition of the stable primary, galactic source

nuclei, from Carbon to Iron and Nickel are surprisingly similar to the

corresponding relative abundances of solar system matter. Surprising

because cosmic ray matter is modern (not more than 10-20 million

years), whereas solar system matter was formed more than 4 billion

years ago. Thus, at present the cosmic ray analysis does not support a

dramatic elemental evolution of the interstellar medium over this wide

span of time.

Radioactive decay isotopes provide information on the time

between nucleosynthesis of cosmic ray nuclei and their initial

acceleration, or time of propagation in galactic magnetic fields (i.e.

cosmic ray age). For example, since Beryllium is rare in nature, its high

abundance in the cosmic rays is due to its secondary production in the

interstellar medium. The spallation processes produce known relative

abundances of stable ''Be and ^Be and of radioactive i*'Be with half-life of

1.6 million years. Thus, from the amount of ^"Be that has decayed

relative to the stable ^Be, we obtain an age for the galactic containment

of the high-energy radiation of 12 to 18 million years.

1.5 The highest energy cosmic rays

Arrays of ground-based detectors of continually increasing area

have been deployed (such as the MIT collaborations, the Leeds arrays

and the world's largest array in Akeno, Japan) to capture the shower

particles and deduce the energy of the incoming primary radiation. These

arrays have produced an energy spectrum, shown in generic form in

region "C", Figure 1.4, that extends to at least 3 x lO^^ electron volts -

the highest energy known for any particle in the universe. These

particles are certainly not containable in magnetic fields in our galaxy.

On the other hand, in their intcrgalactic travel they collide with the

universal cosmic microwave background radiation and lose energy, which

results in their effective propagation distance being limited to less than

about 100 mega-parsecs, a short distance on the scale of the universe.

If they are nuclei of unknown composition or an unknown kind of

radiation and with uncertainties in their direction of arrival, these

highest energy primaries are one of the exciting areas for experimental

and theoretical research in the near future.

1.6 Cosmic rays in interplanetary space

Our Sun influences and shapes the region of the interplanetary

medium. In this region, renamed the Heliosphere, physical conditions are

established, modulated and governed by the Sun. When galactic cosmic

rays come in this region, they are influenced by the Sun's magnetic field

and they get modulated on various time scales. In subsequent sections,

the observed variations of cosmic ray intensity and the effects of solar

influence on these are discussed (see Venkatesan and Badruddin, 1990),

1.6.1 Short-term cosmic ray intensity decreases

Short-term decreases in cosmic ray intensity observed by ground-

based detectors are, in general, broadly classified into two categories:

1.6.1.1 Forbush decreases

Forbush decreases (generally non-recurrent) associated with

transients on the Sun are characterized by a rapid reduction (within a few

hours) in cosmic ray intensity followed by a slow recovery typically lasting

several days (Forbush, 1938). The study of Forbush decreases has

assumed considerable importance, particularly with the resurgence of an

earlier concept that the cumulative effect of Forbush decreases can

account for the - 1 1 year (long-term) variation of cosmic ray intensity

(Lockwood and Webber, 1984).

1.6.1.2 Recurrent cosmic ray intensity decreases

Generally, recurrent (corotating) decreases are associated with

corotating high-speed solar wind streams from coronal holes

(Venkatesan et al., 1982) and has a period of- 27 days.

1.6.2 Long-term variations

Solar wind expands and flows continuously from the Sun into

interplanetary medium; the magnetic field associated with it varies both

in time and space according to the solar conditions. The cosmic rays being

charged particles are affected by the magnetic field variations. On the

scale of years, two prominent variations in cosmic ray intensity are those

related to the - 1 1 year period of solar activity revealed by the sunspot

number and the - 22 year period of the solar magnetic polarity cycle.

1.6.3 Daily variation

Daily variations in cosmic ray intensity arise from spatial

anisotropies in interplanetary space. Ground based detectors record

these once every day as their asymptotic cone of acceptance sweep

through the direction containing the spatial anisotropy. Daily variations

can be studied by the use of harmonic analysis. First harmonic represent

the diurnal variation, second harmonic represent the semi diurnal

variation and so on.

1.6.3.1 Diurnal variation

The solar diurnal variation of the cosmic ray intensity was

interpreted initially on the basis of an outward radial convection and an

inward diffusion along the interplanetary magnetic field (IMF). The

balance between convection and diffusion generates an energy

independent anisotropic flow of cosmic ray particles from the 18-00 hour

CO rotational direction. However, this is a much simple picture. Many

observed features of the diurnal variation had provided an evidence for

additional effects contributing to the diurnal anisotropy (Ananth et al.,

1974; Kane, 1974, 1975; Agrawal and Singh, 1975; Yadav and

Badruddin, 1983a, 1983b; Ahluwalia and Riker, 1985). Theoretical

modelers have introduced a drift concept in the modulation theories to

make it adequate (see chapter 3).

1.6.3.2 Higher harmonics of daily variation

The higher harmonics of daily variation with periods of 12, 8 and 6

hours (semi-, t r i - and quart-diurnal) have also been investigated. The

existence of at least the second and the third harmonics has been

confirmed (Elliot and Dolbear, 1950; Sarabhai and Nerurker, 1956;

Katzman and Venkatesan, 1960). Abies et al. (1965) pointed out that the

direction of maximum of semi-diurnal component in free space (about

03^00 local time) was very nearly perpendicular to the average direction of

the IMF (09:00 or 21:00 local time). Subramanian and Sarabhai (1967)

and Quenby and Lietti (1968) have provided an explanation for the

observed semi-diurnal variation in terms of the cosmic ray gradient

perpendicular to the ecliptic plane.

CHAPTER - 2

The interplanetary medium

/•

/ > t

CHAPTER-2

THE INTERPLANETARY MEDIUM

2.1 Solar wind and Inteiplanetary magnetic field (IMF)

The solar wind is the continuous outflow of completely ionized gas

from the solar corona. It consists of protons and electrons, with an

admixture of a few percent alpha particles and much less abundant

heavy ions in different ionization stages. The hot corona typically has

(base) electron and proton temperatures of 1-2 million Kelvin and

expands radially outward into interplanetary space, with the flow

becoming supersonic within a few solar radii. Because the solar wind

plasma is highly electrically conductive, the solar magnetic field lines are

dragged away by the flow, and due to solar rotation are wound into

spirals. This magnetic field forms the interplanetary magnetic field

(IMF). The wind attains a constant terminal speed, and its density then

decreases radially in proportion to the square of the radial distance.

At 1 AU the average speed of the solar wind is about 400 km/s.

This speed is by no means constant. The solar wind can reach speeds in

excess of 900 km/s and can travel as slowly as 300 km/s. The average

density of the solar wind at 1 AU is about 7 protons/cm^ with large

variations. Flux of solar wind particles at 1 AU is 500 x 10^ particles per

square centimeter per second. At this distance, the thermal energy is

around 10 eV. Protons have kinetic energy 1000 eV and electrons have 10

eV. Magnetic field in the solar wind at 1 AU is around 5 x 10" ^ gauss.

The hot coronal plasma of the Sun (solar wind) has a high

electrical conductivity and, therefore, it carries the solar magnetic field

lines into the interplanetary space, but with the roots of the lines fixed

on the rotating Sun. The frozen-in magnetic field lines do not allow the

plasma to diffuse across them. They connect all plasma originated from

the same position on the Sun, and thus form an Archimedean spiral in

the interplanetary space (see Figures 3.1 and 4.1).

The equation of the Archimedean spiral can be derived (Kallenrode,

1998) from the displacements Ar and A^. If we assume as initial

conditions of the plasma parcel on the Sun a source longitude ^^ and a

source radius r^, at a time t the parcel can be found at the position

<PiO = ft>™„ .t + (PQ a n d r{t) = M „„, .t + r,.

Eliminating the time yields the equation for the Archimedean spiral:

^Zl^ + r n^

With y/ = oy,^„r Iu^^^^,^ , the path length s along the spiral is given as

1 u 2 CO,.,,

(^•V^' + 1 + In {/ + V^'+l}) (2)

The magnetic field in the equatorial plane can be expressed in

polar coordinates B = (B^,B^). The magnitude of B depends on the radial

distance only, thus it is \B\ = B(r). Gauss's law in spherical coordinates

yields

V j = 4 | - ( r ' 5 , ) = 0 (3) r •' dr

or r^B^ -r^oB^ . Thus the magnetic flux through spherical shells is

conserved and the radial component of the field decreases as

B.=B, 'o

V ' y

(4)

Since the Magnetic field is constant, it is dB/dt = 0. From the frozen-in

condition: — - V x (w x 5) = - ^ V 'S , (5) dt ATTG

(Equation (5) allows to determine how a given velocity field u deforms a

magnetic field B), we then get V x (M x 5) - 0 , or in spherical coordinates

- ^ ( K ^ 5 , - M , 5 ^ ) - 0 . (6) r or

Thus we have r{u^B^ -u^B^) = const. Assume ro to be at the source

surface. There B is radial and we get

ru^B^ - ru^B^ = r.u^^^B^ =r\co^^„B,. (7)

In the second step, the rotation speed of the Sun was used to describe the

azimuthal component of the solar wind speed at the source surface. From

the expression (7), the azimuthal component of the magnetic field is

2

This can be approximated as B^--rco^^„BJu^ for large distances

{rco^^^ >u^). The azimuthal component therefore decreases with 1/r while

the radial component decreases as l/r^. The field strength decreases with

r as

5(r)^^Jl V ". J

(9)

The angle y/ between the magnetic field direction and the radius vector

from the Sun is tan <p = B^ / B^. For large distances this reduces to

tan^ = a> .„„r/w . At the earth's orbit, tan ^ is about 1 for typical solar

wind conditions, and thus the field line is inclined by 450 with respect to

the radial direction. This is known as the garden-hose angle because the

similar effect can be observed with a rotating sprinkler; thus the

deformation of the field lines is also called the garden-hose effect.

2.2 Impacts of solar and interplanetary phenomena at the Earth

The Sun has very serious impacts on interplanetary space and the

environments of planets (Dwivedi, 2003).

Near the solar poles the magnetic field lines are open and solar

plasma flows continuously into space creating there the fast solar wind

11

blowing around the Earth deep into outer regions of the planetary

system. Some region of the corona appear dark where the coronal gas is

much less dense and less hot than usual; these regions are called coronal

holes (Figure 2.1) and are responsible for solar wind streams. At lower

latitudes, coronal helmet streamers and possibly active regions during

periods of field-line openings are sources oi slow solar W7i2<i (Figure 2.2).

Fig. 2.V- Coronal hole

Fig. 2.2- Schematic diagram showing region of fast and slow solar wind from the Sun and some other features of interplanetary medium.

Streams of accelerated particles, both electrons and atomic nuclei,

propagate at various places through interplanetary space. And in

addition to these streams of plasma and particles, coronal mass ejections

Fig. 2.3: Coronal mass ejection (CME)

(plasma ejection from the Sun? are main cause of geomagnetic storms on

Earth) send plasma clouds and shock waves in various directions

through interplanetary space and eventually cause other particle

accelerations there. All this creates highly variable and very complex

conditions in the space between the Sun and the Earth and in the last

decade people began to speak about, and regularly study, the space

weather.

Solar flare, a source of X-rays, influences Earth's ionosphere and

thus cause disturbances in radio communications around the Earth. A

major eruptive (long-decay) flare can disturb radio contacts for many

hours.

13

The most energetic flares emit protons with energy exceeding 500

MeV which arrive at the Earth some 15 minutes after the flare onset,

produce streams of neutrons in Earth's atmosphere, and cause the so-

called ground level effects (GLEs). Flares that produce protons of such

high energies are sometimes called cosmic—ray flares. Flares that emit

protons with energies higher than 10 MeV are often called proton flares.

Particles of lower energy are guided by the Earth magnetic field to the

polar regions and cause there absorption of radio waves (polar cap

absorption) and intense aurorae. All these effects are delayed by tens of

minutes to several hours after the flare onset, depending on the energy of

the propagating particles.

Before the discovery of coronal mass ejections (CMEs) in the

seventies, all effects of the Sun on the magnetosphere were ascribed to

major solar flares. Coronal mass ejection (Figure 2.3), often with a shock

wave, arrives at the Earth, if it propagates in the right direction toward

us. This arrival - two or three days after its origin on the Sun - has a

strong impact at the Earth's magnetosphere and causes a geomagnetic

storm which sometimes can last for several days and has serious impact

on communications all around the Earth. Now, it is known that the real

agent that causes geomagnetic storms are CMEs, which can originate

also in quiet parts of the Sun, without any observed chromospheric flare.

Flares are excellent indicators of coronal storms and actually indicate the

strongest, fastest, and most energetic disturbances coming from the Sun.

The largest geomagnetic storms are caused by fast CMEs, which usually

are associated with flares, while moderate or small storms mostly have

no association with flares (Webb, 1995). Flares are also sources of short­

wave radiation that affects the ionosphere, and produce a significant

fraction of accelerated particles that cause disturbances in space and at

the Earth.

Active processes on the Sun also influence the weather at the

Earth, but these effects are indirect - depending on the behavior of the

magnetosphere and ionosphere and on the meteorological situation at the

time of the disturbance arrival - so that they are very complex.

14

2.3 Magnetic domain of the interplanetary space:

The Heliosphere

Heliosphere is the region of space where the solar wind's

momentum is sufficiently high that it excludes the interstellar medium.

The solar wind plasma thus dominates this region.

As the solar wind expands, its density decreases as the inverse of

the square of its distance from the Sun. At some large enough distance

from the Sun (in a region known as the heliopause), the solar wind can

no longer "push back" the fields and particles of the local interstellar

medium and the solar wind slows down from 400 km/s to perhaps 20

km/s. This transition region is known as heliospheric termination shock.

Beyond the termination shock, a pressure balance exists between the

Local Interstellar Medium (LISM) and the solar wind, through a surface

called the heliopause. It is possible (although not proven as yet) that the

interstellar wind (corresponding to the motion of the heliosphere through

the LISM) may be fast enough to generate a shock wave, the heliospheric

bow shock, upstream of the heliopause (Figure 2.4).

200 -250 AU

INTERSTELLAR WIND

TERMINATION

HELIOSPHERIC BOW SHOCK

Fig. 2.4: A schematic representation of various region of the heliosphere.

Actually, heliosphere extends from the solar corona to an outer

boundary where the solar wind encounters the interstellar medium

15

(Parker, 1958). The outer corona of the Sun consists of a fully ionized gas

threaded by magnetic fields rooted in the visible surface of the Sun, the

photosphere. The coronal plasma is very hot, with a temperature in

excess of a million degrees. It is still unclear just how the corona is

heated to such temperatures! the most likely explanation is that waves

from the lower layers of the solar atmosphere provide the necessary

energy to heat the corona. The energy deposited in the coronal plasma

appears also to be sufficient to accelerate it away from the Sun in the

form of the solar wind. The speed of the solar wind varies between about

300 km/s to more than 800 km/s. This speed is well in excess of the speed

of sound in the plasma.

Polarity of the heliosphere changes after every 11 years. The

approximately 11-year solar activity cycle is reflected in the strength of

the IMF, the frequency of coronal mass ejections (CMEs) and shocks

propagating outward, and the strength of those shocks. The solar

magnetic field reverses at each solar activity maximum, resulting in 22-

year cycles as well. The field orientation is known as its polarity and is

positive when the field is outward from the Sun in the northern

hemisphere (e.g. during the 1970s and 1990s) and negative when the

field is outward in the southern hemisphere (e.g. during the 1960s and

1980s). A positive polarity field is denoted by A > 0 and a negative field

by A < 0.

HELIOPAUSE

.•INTERSTELL ••• MEDIUM

POSSIBLE BOW SHOCK

INTERSTELLAR MEDIUM

MAGNETIC FIELD LINES

Fig. 2.5: Schematic diagram of heliosphere

Galactic cosmic rays beyond the Heliosphere are considered to be

temporally and spatially isotropic, at least over timescales of decades to

centuries. Galactic cosmic rays get modulated when they come in

Heliosphere. It is likely that the Heliosphere is not spherical but that it

interacts with the interstellar medium as shown schematically in Figure

2.5. Cosmic rays enter the Heliosphere due to random motions, and

diffuse inward toward the Sun, gyrating around the interplanetary

magnetic field (IMP) and scattering at irregularities in the field. They

will also experience gradient and curvature drifts (Isenberg and Jokipii,

1979) and will be convected back toward the boundary by the solar wind

and lose energy through adiabatic cooling, although the latter process is

only important below a few GeV and does not affect ground-based

observations. The combined effect of these processes is the modulation of

the cosmic ray distribution in the Heliosphere (Forman and Gleeson,

1975) (see details in Chapter 3).

2.3.1 Size of Heliosphere

Given the existence of the continuous flow of the solar wind, how is

the outer boundary of the Heliosphere determined? A simple sketch of

the Heliosphere and related phenomena in Figure 2.4 provides an outline

of the very complex answer to this question.

In the first place, the solar wind eventually slows down," this

occurs through a shock wave, the so-called termination shock, where the

solar wind speed falls below the sound speed. The location of this

transition region (called the heliospheric termination shock) is unknown

at the present time, but from direct spacecraft measurements, must be at

more than 50 AU. In fact, in 1993 observations of 3 kHz radiation in the

outer Heliosphere (Kurth et al., 1984) by plasma wave receivers on

Voyagers 1 and 2 have been interpreted as coming from a radio burst at

the termination shock. This burst is thought to have been triggered by an

event in the solar wind observed by Voyager 2. From the time delay

between this triggering event and the observation of the 3 kHz

radiations, the distance of the termination shock has been put between

130 and 170 AU.

17

•

. • • • . • * • ' ' .

rn (TJ . TBE I."?

C <B § J^ V » ^ - i / * ! _ . . W

§ . . - . - , » -.^---«- , •,-. Aatorold

B B K .

Heliosphere

..'~2 ~ 3 - i . ' . " ' i - ' 4 ., «5 " ^ ^ ^ , JL; 10 10 Ediii 1 0 •'0 10

^ g ^ ^ ^ ^ ^ ^ B • ^-^^ GCioud?

Interstellar Medium ^

Fig. 1.6: Size of heliosphere compared with various objects. Lengths are in AU.

No space probe has yet reached the termination shock, although

Voyager 1, now at some 80AU from the Sun is thought to be getting close

to it.

2.3.2 Heliospheric neutral sheet

The expanding solar wind plasma carries with it the interplanetary

magnetic field (IMF). A neutral sheet separates the field into two distinct

hemispheres, one above the sheet, with the field either emerging from or

returning to the Sun, and the other below the sheet, with the field in the

opposite sense.

The solar magnetic field is not aligned with the solar rotation axis and

is also more complex than a simple dipole. As a result, the neutral sheet is

not flat but wavy, rotating with the Sun every 27 days. At solar minimum,

the waviness of the sheet is limited to about 10° helio-latitude but near solar

maximum the extent of the sheet may almost reach the poles. With the

rotation of the sheet every 27 days, the Earth is alternately above and below

the sheet and thus in an alternating regime of magnetic field directed toward

or away from the Sun (but at an angle of 45° to the west of the Sun-Earth

line).

Fig. 1.7: Schematic diagram of neutral sheet

This alternating field orientation at the Earth's orbit is known as the

IMF sector structure. The neutral sheet structure is such that there are

usually two or four crossings per solar rotation.

An inclined current sheet has a significant effect on the global

heliospheric field and on the drift motions of the cosmic rays. These

implications were pointed out by Jokipii, who proceeded to include drift

effects in the basic transport equation (see chapter 3 for details) used to

describe the behavior of energetic particles (Jokipii et al., 1977). In

particular, the heliospheric current sheet (HCS) was shown to cause fast

drifts along it and to act as a major source or sink of cosmic rays in the

heliosphere (depending on the polarity of the fields above and below it, which

change sign from one sunspot cycle to the next). The influence of the HCS

was evident in the model as a correlation between cosmic ray intensity and

19

the changing inchnation of the current sheet. This aspect of the model was

shown to be consistent with observations (Smith, 1990). Other importance of

the HCS is its close relation with plasma parameters. Since the HCS serves

as a magnetic equator, many solar wind properties are organized with respect

to it. Studies of various plasma parameters, including solar wind speed,

density, temperature, and composition, show a close correlation with the

current sheet (see Smith, 2001 and references therein).

20

CHAPTER - 3

Solar modulation of galactic cosmic rays

CHAPTER-3

SOLAR MODULATION OF GALACTIC COSMIC RAYS

3.1 Solar modulation: Basic processes

In the local interstellar region, outside the heliosphere, the

distribution of galactic particles is considered almost isotropic in space

and time. Due to random motion and collisions these particles cross the

boundary and enter the Heliosphere. They gyrate around the IMF but

due to small-scale irregularities in the IMF the particles are scattered

from their gyro-orbits. The overall motion of the particles will be seen as

diffusion from the boundary towards the Sun. Along their diffusive

journey the particles will also undergo gradient and curvature drifts in

the IMF (Isenberg and Jokipii, 1979). The solar wind, with the IMF

frozen into it, also convects particles back towards the heliospheric

boundary. The overall result of these processes is solar modulation

within the Heliosphere of the galactic distribution of cosmic-ray particles

(Forman and Gleeson, 1975).

In this way, there are four physical processes, which are believed

to be important for modulation: diffusion, effects associated with the

large-scale magnetic field, convection, and energy change (adiabatic

cooling). They are discussed below in brief.

3.1.1 Diffusion

The magnetic field in the solar wind contains small-scale

irregularities. There are Alfven waves, perhaps some magetosonic waves,

and other fluctuations. In some cases these irregularities have scale sizes

comparable to the gyroradii of the cosmic rays, with the result that the

cosmic rays are scattered. Their pitch angle or equivalently their velocity

parallel to the mean magnetic field changes randomly with time. It is

also possible for the particles to be scattered or to propagate by other

means, in a random fashion, in a direction normal to the mean magnetic

field (Jokipii and Parker, 1969).

21

3.1.2 Effects due to the large-scale magnetic field

Due to the rotation of Sun, its field is spiral. The spiral is tightest in the

equatorial plane of the Sun where the rotation effects are most important

(see Fig. 3.1). However, as we increase in latitude the spiral becomes less

Fig.3.1: A schematic drawing of the pattern of the mean magnetic field in the Heliosphere.

tightly wound, and, in fact, the field becomes radial over the solar poles.

The orientation, then, and also the magnitude of the magnetic field in the

heliosphere vary systematically with radial distance and latitude. Hence

cosmic rays have an easier access to the inner Heliosphere over the solar

poles than they do near the equatorial plane.

Another important effect associated with the large-scale field is

gradient and curvature drift. The orientation and magnitude of the

magnetic field varies with radial distance and latitude. Thus, particles

may undergo systematic drifts in this field, which among other effects

should result in a significant transport of particles in latitude (Isenberg

and Jokipii, 1979 and Jokipii et al., 1977). The direction in which

particles drift depends on the polarity of the magnetic field (see section

3.2.1).

22

3.1.3 Convection

The speeds of the waves, which scatter the particles and cause

them to diffuse, are very much less than the solar wind speed. The waves

are thus convected outward with the solar wind, and in turn tend to

convect the cosmic rays out of the Heliosphere. Indeed, it is the effect

which gives rise to the modulation. Neither of the two previous effects,

diffusion or drift, would by themselves cause a reduction in the galactic

cosmic-ray intensity in the inner Heliosphere.

3.1.4 Energy change

The cosmic rays, as for as the solar wind is concerned, are a highly

mobile gas which exerts a pressure. And since there are more cosmic rays

in the interstellar medium than in the inner Heliosphere, this pressure

has a positive gradient. The solar wind, then, which blows outward, does

work against this pressure gradient and imparts energy to the cosmic

rays. However, as for as the cosmic rays are concerned, they find

themselves in an expanding medium. The solar wind blows radially from

the Sun, and thus diverges or expands as it goes outward. The cosmic

rays, which are rattling around in the wind, expand along with it, and are

adiabatically cooled (Parker, 1965).

3.2 Solar modulation^ Theoretical models

As already described, four processes together are responsible for

the modulation of cosmic rays in the Heliosphere. However, adiabatic

cooling is effective only for particles having energy less than few GeV,

hence this effect can be neglected for ground level studies. Irregularities

in IMF make particles to diffuse (towards Sun) parallel and normal to the

field. The same scattering mechanism is partly responsible for the

convection of particles outwards from the Sun by the solar wind.

The curvature of the IMF lines and the gradient in field intensity

leads to drift velocities of the cosmic-ray particles in the interplanetary

23

medium. All these mechanisms combine to produce the solar modulation

of galactic cosmic rays.

Modulation theories attempt to model the effect of Sun's IMF on

the distribution of the galactic cosmic rays in the Heliosphere. The

theoretical basis of modulation was formalized by Forman and Gleeson

(1975). The treatment of the distribution function of cosmic rays from

which the theory is derived was given by Isenberg and Jokipii (1979). A

brief description (Hall et al., 1996) is as follows^

If F(x, j j , t) is a distribution function of particles such that

p2F(je, ^ , t )d3xdpdQ

is the number of particles in a volume d^x with momentum p to p + dp

centered in the solid angle dQ then it can be shown (Isenberg and jokipii,

1979) that

^ + V.5 = 0, (1) dt

where

U(x,p,t) = p^ JF{x,p,t)dQ. 4)!

and S is the streaming vector:

1 + (COT) \ + (a)T)

and CO, gyro-frequency of the particle's orbit; x, mean time between

scattering; K, (isotropic) diffusion coefficient; C, Compton-Getting

coefficient (Compton and Getting, 1935 and Forman, 1970); B, unit

vector in the direction of the IMF; r, the radial direction of a coordinate

24

system centered on the Sun! V, solar wind velocity; and U, number

density of particles.

Adiabatic cooling has not been included in Equation (l) as it is

relatively unimportant above a few GeV. The first te rm of Equation (2)

n tiai-»T»i n o c f n o r m f \ n r a v r i nri-n\7Cini-irfn riT f n o rvQT ' f i r ' l oG K\r -i-ViO o r i l o -p ^xnr»r] fV to

second term describes parallel diffusion, the third describes

perpendicular diffusion and the fourth involves the gradient and

curvature drifts. Writing Equation (2) in te rms of a diffusion tensor

S = CUV-i£.{VU), K =

K , K-r J.

0 0

0 ^

0

K

(3)

IIJ

where KJ^ , ic,j, are respectively the perpendicular and parallel diffusion

coefficients and the off-diagonal elements, /c,,, are related to gradient and

curvature drifts (see Isenberg and Jokipii, 1979, and Equation (5) below),

then

— = -V.(CUV-ic.'^U). dt =

(4)

Equation (4) is a s tandard time dependent diffusion equation. It is

commonly called the transport equation because if we note t ha t

[dt)

= V.{>c'\VU) + {V.ic'){VU) (5)

V.(/c^V[/) + F^.V/7

25

where {dU/ dtY refers to only the non-convective terms in Equation (4)

and K and K^ refer to i£ being split into symmetric and anti-symmetric

tensors, one finds that V.K^ is the drift velocity (F^,) of a charged particle

in a magnetic field which has a gradient and curvature. Equation (4) is an

equation explicitly representing the transport of cosmic rays in the

heliosphere by convection, diffusion and drifts as mentioned earlier.

3.2.1 Predictions of models

Jokipii and co-workers presented some results by numerically

solving the transport equation (equation (4)) for U(x,p,t).

Jokipii et al. (1977) and Isenberg and jokipii (1978) showed that

because the IMF is characterized by the two distinct polarity

configurations over 22 years the drifts would have opposite effects on

modulation in these two states while diffusion mechanisms do not depend

on the IMF polarity. In A > 0 IMF polarity states particles will essentially

flow into the Heliosphere from the high latitudes and travel out of the

Heliosphere along the heliospheric equator (see Figure 3.2).

A<0

highly irregular, B field

Ttrmination /shock

palhs

enhanced scattering

iSM FLOW

Fig. 3.2: Cosmic ray drift patterns during two polarity epochs.

26

During the A < 0 IMF polarity states the net effect of drifts is to cause

particles to travel from the outer regions of the Heliosphere along the

helio-equator towards the Sun and exit the heliosphere via the polar

regions.

Jokipii and Kopriva (1979) predicted that these drift effects

(coupled with the diffusion of particles) would lead to a larger radial

gradient of particles during A < 0 epochs than in A > 0 epochs. The model

also suggested that the general route traveled by cosmic rays during the

A > 0 magnetic polarity states would cause a minimum in number

density at the neutral sheet for these epochs while the transport of cosmic

rays during the A < 0 magnetic polarity states would result in the density

of particles being a local maximum at the equator and a minimum at

some higher heliolatitude. They predicted that this would be observable

as a bi-directional (symmetric about the helio-equator) latitudinal

gradient, which reverses direction after every IMF polarity reversal.

27

CHAPTER - 4

* Anisotropic cosmic * ray modulation

/> t

CHAPTER-4

ANISOTROPIC COSMIC RAY MODULATION

In Chapter-1, a brief description of cosmic ray modulations on

various time scales has been given: Short-term Forbush decreases,

recurrent decreases and long-term variations are isotropic while diurnal,

semi-diurnal variations are anisotropic. Out of these only Forbush

decreases are non-periodic while others are periodic variations.

4.1 Diurnal Anisotropy: Basic concepts and its importance

The average hourly count rate of a cosmic-ray detecting

instrument from a series of complete solar days shows an approximately

sinusoidal variation with a period of 24 hours. Harmonic (Fourier)

analysis of the data will yield the time of maximum (phase) and

amplitude of the variation, with the amplitude usually being expressed

in terms of a percentage deviation from the mean hourly - count rate.

Following the discovery that the solar diurnal variation in cosmic-

ray data was related to a spatial anisotropy in the primary cosmic-ray

distribution (Elliot and Dolbear, 1951) this anisotropy has continued to

be vigorously studied. By the mid-1960s 30 years of ionization chamber

data in 2- and 1-hour intervals had been collected and a concentrated

effort to understand the solar diurnal variation and the processes

responsible for producing the associated anisotropy in galactic cosmic

rays had begun.

Figure 4.1 gives a basic idea of the diurnal anisotropy. Earth's

rotation causes the asymptotic cone of view of an instrument to sweep

through the anisotropy once a day. This gives rise to a diurnal variation

in count rate data with a time of maximum around 18^00 local time.

Rao et al. (1963) defined the asymptotic cone of acceptance as 'the

solid angle' containing the asymptotic directions of approach (The

asymptotic direction of approach is the direction that a cosmic-ray

particle is traveling (in free space) before it is deflected by the Earth's

28

magnetic field) that significantly contributes to the counting rate of a

detector. It had been realized that the acceptance cone of a recording

instrument depends on its physical dimensions, position on the Earth

and the geomagnetic field. The asymptotic cone of a detector is never

immediately along the axis, which the instrument is aligned and this

causes the recorded phase of the diurnal variation to vary from station to

station. By taking account of the asymptotic cones of acceptance of

individual instruments, Rao et al. concluded from two years of neutron

monitor data that the solar diurnal anisotropy had an invariant

amplitude and phase in free space and was caused by an anisotropic

streaming of particles coming from somewhere close to 90" east of the

Earth-Sun line.

Fig. 4.1: Solar diurnal anisotropy in the local time-coordinate system.

Early modelers recognized that by neglecting drift terms and other

effects such as perpendicular diffusion, vector addition of the remaining

streaming components would lead to an overall streaming of particles in

a direction parallel to the Earth's orbit around the Sun. The particles

29

would seem to corotate with the Sun. This corotating streaming (or

anisotropic flow) of particles could be observed as a diurnal variation in

the count rate of a cosmic-ray detector as the detector's viewing cone

rotated through 360^ of space in one day. The anisotropy is the solar

diurnal anisotropy. The anisotropy, manifested as a diurnal variation,

would have the time of maximum count rate outside the magnetosphere

(phase) at 18-00 local solar time (streaming along the tangent to the

Earth's orbit; see Figure 4.1).

Parker (1964) proposed that corotation was a combination of the

random walk (scattering by magnetic irregularities) of particles in the

IMF and an electric field drift velocity. Forman and Gleeson (1975) built

on this model and produced the present theory (Equation (2), Chapter-3).

They showed that pure corotation would arise if there were no net radial

streaming (and drifts are considered negligible). Their model implied

that the magnitude of the solar diurnal anisotropy is 0.6% of the average

isotropic background flux of cosmic rays. If perpendicular diffusion is not

neglected the amplitude of the anisotropy will be less than 0.6% and will

be a function of the relative importance of perpendicular and parallel

diffusion.

Levy (1976) included the curvature and gradient drifts in a model,

which showed that these drifts could be responsible for changing the

direction of the anisotropy in alternate solar cycles. This could explain

the observed 22-year cycle in the anisotropy. A similar result was

obtained by the model of Erdos and Kota (1979). Their model predicted

that the direction of streaming during A < 0 IMF polarity states should

be along the direction of the Earth's orbit. Drifts included in this model

were considered responsible for the model indicating that the streaming

should change direction during the next IMF polarity state and this

streaming would be observed as a diurnal variation with a phase around

15:00 in local solar time. This model predicted that the anisotropy's

amplitude and phase would be insensitive to rigidity but the amplitude

would be sensitive to the neutral sheet warp.

If ^ symbols the anisotropy of cosmic rays in the heliosphere,

35* ^ = — (Gleeson, 1969), and defining i a n d i i n the ecliptic plane with

vU

z along the direction of the IMF away from the Sun, it can be shown

30

(Bieber and Chen, 1991) that transforming the gradient vector into a

spherical coordinate system centered on the Sun the component of ^ in

the coordinate system are^

x = 4 sin X - KGr sin X + pGe sgn(5)

^ =sgn(5)pG,sinj + /l G, •I'-'o (1)

4 =4cos;r-/l;/G,cos;!r

where ^ ,, Compton-Getting anisotropy (3CV/v) (Compton and Getting,

1935); X, angle of the IMF with the Earth-Sun line; 0, unit vector in the

direction of increasing solar co-latitude; p, gyro-radii of the particles; Gr,

radial gradient of cosmic-ray density; Ge, latitudinal gradient of cosmic-

ray density; V, solar wind speed; and v, speed of the cosmic-ray particles.

Sgn (B) represents the effects of drifts on anisotropy. Its value is 1

if the position of Earth in the neutral sheet is such that the IMF is

directed away from the Sun; otherwise is - 1 .

Equation (l) describes the anisotropy of cosmic rays in the three-

dimensional heliosphere. In that coordinate system, components in

ecliptic plane ( x, z) are the components of the anisotropy of cosmic rays

responsible for the solar diurnal anisotropy (£,SD).

In the absence of other anisotropies, the space distribution F(x) of

the solar diurnal anisotropy can be represented as the first order

ordinary Legendre polynomials (Nagashima, 1971):

F{x) = risDPxi.^^^X\ (2)

where

^so - F(X)G{P)

and

G{P) =

r DV

V i u y

p<p.. 10.

0, P>P.

(3)

31

Here, P is the rigidity and Pu is the rigidity where the anisotropy ceases

to be significant.

After further corrections (Nagashima and Ueno, 1971), the form of

space distribution F becomes-

where {6j^,aj^) are the co-declination and right-ascension of the reference

axis of the anisotropy (in the azimuthal direction around the Sun in the

ecHptic plane), {Oj,aj) are the co-declination and right-ascension of the

particles' arrival direction and

f"{ej,,a^,ej,a,) = P^J c o s | L „(cos^^)cosw(«^ -«^) (5)

where Pn,m(x) are the associated Legendre polynomials.

The space distribution F(x) will produce two space harmonic

components (zeroth and first orders). The zeroth order space harmonic

component is along the rotation axis of the Earth and is constant. The

first order space harmonic component (SsoCt)) is directed parallel to the

Earth's equator:

^nsijoos—itj-t^) (6)

ITT . In = x.-n COS—t. + y,.„ sm — /,

where

VsD =i(XsDf+(ySDf

24 t^ = —arctan

a = — 24

^X. ^ SD

V ^ . s v j ;

(7)

32

The free-space harmonic component SsD(t) will produce the solar

diurnal variation D(t) in an instrument's count rate at Earth. Fourier

analysis can be used to derive the components of this variation.

We have discussed that how the solar diurnal anisotropy is caused

by solar modulation of the galactic cosmic rays in the heliosphere.

Long-term averages of the solar diurnal variation provide information

about the average behavior of cosmic rays in the vicinity of the Earth.

Since the diurnal anisotropy is caused by solar modulation, one can use

the effect to derive information about the underlying modulation

processes (e.g. see Hall et al., 1996 and Venkatesan and Badruddin,

1990). Following the discovery that solar diurnal variation in cosmic ray

data was related to spatial anisotropy in primary cosmic ray distribution

(Elliot and Dolbear, 1951), this anisotropy has continued to be studied

(Rao et al., 1972; Forbush, 1973; Agrawal and Singh, 1975; Duggal et al.,

1979; Yadav and Badruddin, 1983a; Badruddin et al., 1985; Bieber and

Chen, 1991; Ahluwalia and Sabbah, 1993; Ananth et al., 1993; Swinson,

1993; Hall et al. 1997; Munakata et al., 1997; Sabbah, 1999).

In this study, a detailed investigation of the solar activity and

solar magnetic cycle dependence of the diurnal anisotropy over the period

of almost five solar cycles (19-23) has been done and the behavior of

diurnal anisotropy in the light of simulations of modulation including

drift effects and tilt of heliospheric current sheet has been interpreted.

4.2 Harmonic Analysis

Harmonic (Fourier) analysis has been done to derive the vector of

diurnal anisotropy because a periodic variation can always be studied by

means of it. In many cases, particularly in cosmic rays, the phenomenon

whose variation is to be studied is not strictly periodic. Thus if the

numbers to be analyzed represent hourly mean of cosmic ray intensity,

the mean for 0** hour will not, in general, be the same as the means for

24*'' hour. This difference is (which on account of secular changes etc.)

allowed for in practice by applying a correction (known as Trend

Correction) to each of the terms (i.e. 24 ordinates).

33

Let V, be the trend corrected value at x = — * 12

and y^. be the uncorrected value

'±Sy then, y, = y. •xk

24 J

where ±5y is the secular change (i.e., ±3\> = y.^^ - y^).

Formulism of Harmonic analysis is given below in brief

Any 2-71 - periodic function f(x) is the sum

CO

OQ + ^ ( a i coskx + bj^ sin Ax)

of its Fourier series. The coefficients ao, ak and bk are calculated by

OQ = — \f{x)dx, a,^-— \f{x)cos{kx)dx, b,^=— \ f {x) sin{kx)dx

The amplitude rk and phase (()k of the k'*' harmonic are expressed as

^k = V K ' + ^ t ' ) ' <l>k =tan' \^kj

Where r gives the amplitude of the anisotropy vector and (|) gives its

phase. Phase represents the time of the maximum of anisotropy.

Although it is a local time variation, the daily variation ought to be

referred to universal time to simplify comparisons between points of

observation with big differences in longitude.

4.3 Data analysis

The pressure corrected hourly neutron monitor data of Oulu, Deep

River, Climax and Huancayo with different cut-off rigidities (Table-l),

have been subjected to harmonic analysis to derive the amplitude (in

percent) and time of maximum (in hours), for nearly 50 years during the

period 1955-2003. These neutron monitor stations are so selected that it

covers a major part of the Earth location (in latitude); polar stations are

34

not suitable for study of diurnal anisotropy. Further, care has been taken

that the data of at least two stations is available for every year. The days

associated with large transient cosmic ray intensity variations, Forbush

decreases and ground level enhancements (GLEs) have been removed

fi-om the data analyzed. Then the average amplitude and phase is

obtained for each year of available data and for each station. Further, the

diurnal anisotropy vectors have been examined by plotting them on

harmonic dial after classifying and averaging them into (different)

appropriate groups according to solar cycles, 1955-64 (19), 1965-75 (20),

1976-85 (21), 1986-96 (22) and 1997-2003 (23), and polarity state of the

heliosphere, 1961-70 (A < O), 1971-80 (A > O), 1981-90 (A < O) and 1991-

1999 (A > O). To obtain an insight of the whole spectrum of distribution of

amplitudes and time of maxima on day-to-day basis in different groups,

histogram of respective group of vectors has also been plotted.

Table-1: Summary of the data

Neutron

Monitor

Station

Oulu

Deep River

Climax

Huancayo

Latitude

(degrees)

65.02

46.10

39.37

-12.03

East

Longitude

(degrees)

25.50

-77.50

-106.18

-75.33

Threshold

Rigidity

(GV)

0.78

1.07

2.99

12.91

Data Period

1964-2003

1964-1992

1955-2002

1955-1992

4.4 Results

Figure 4.2 shows the yearly average diurnal amplitudes at Oulu

from 1964 to 2003, Deep River from 1964 to 1992, Climax from 1955 to

2002, and Huancayo from 1955 to 1992. In this figure, solid vertical lines

represent the years of solar activity minima and the period between two

dashed lines around each solar maximum represents the epoch of solar

polar field reversal. It is seen from this figure that the amplitude of the

diurnal anisotropy show an 11-year variations with the lowest values

35

occurring at solar minima and the highest values near solar maxima.

Enhanced amplitudes for one/two years during the declining phase of

each solar cycle are additional noticeable features of long-term plot

shown in Figure 4.2. Specifically, the near periodic enhanced amplitudes

are noticed in the periods 1962-63, 1973-74, 1984-85, 1994 and 2002-03;

periods in the declining phase of solar cycle 19, 20, 21, and 22

respectively. These are the periods when high-speed solar wind streams

from coronal holes are prevalent. Thus it is likely that the enhancements

in average solar wind speed during declining phases of solar cycle are

responsible to increase in amplitudes of diurnal anisotropy.

Enhancements in amplitudes of semi-diurnal and tri-diurnal anisotropy

with increase in solar wind velocity have been reported by Agrawal

(1981).

19 6 0 19 7 0 1 9 8 0

Y E A R 19 9 0 2 0 0 0 2 0 1 0

Fig. 4.2: Yearly mean cosmic ray diurnal anisotropy amplitudes obtained using Neutron Monitor data at four stations, Oulu, Deep River, Climax and Huancayo. Solid vertical lines indicate the years of solar minimum and the periods between two-dashed lines in each solar cycle indicate the epoch of solar polar field reversal.

36

Thus amplitude of the diurnal anisotropy is a clear 11-year solar

cycle variation with minima at or near sunspot minimum. From these

figures it is also evident (see also Table-2) that the diurnal amplitude is

almost independent of cut-off rigidity of the observing station. These

observations indicate that the amplitude of diurnal anisotropy is affected

both by changes in solar activity as well as by co-rotating high-speed

solar wind streams.

Table-2: Diurnal Amplitude (Ai) and Phase (91) during solar minima

Years

1955

1965

1976

1986

1996

Pol­arity Stat e

A>0

A<0

A>0

A<0

A>0

Oulu

Ai (%) *

0.219

0.228

0.176

0.137

(pi (hrs) -

14.98

12.90

14.62

12.89

Deep River

Ai (%) •

0.218

0.253

0.21

"

(91) (hrs) "

14.80

12.58

14.89

" •

Climax

Ai (%) 0.137

0.179

0.198

0.207

0.212

(cpi) (hrs) 14.66

15.29

12.56

15.20

13.01

Huancayo

Ai (%) 0.153

0.115

0.177

0.1

'

(91) (hrs) 11.48

11.61

7.57

9.44

~

The long-term variations in the phase (time of maximum) of the

average diurnal anisotropy for the years 1955 to 2003 are shown in

Figure 4.3. It is seen from the figure that local time of maximum of the

diurnal anisotropy at each location shows a prominent ~ 22-year

variation with minimum occurring in 1955, 1976 and 1997. The phase

shift to earlier hours starts after the solar polarity reverses from

negative (A < O) to positive (A > O) states (e.g. in 1971). This shift to

earlier hours continues till the subsequent solar minimum (1976),

reaching minimum phase at or near solar minimum and then starts

recovering towards the pre-reversal level. Again after ~ 22 years, after

1990 polarity reversal, when the Heliosphere comes to same polarity

37

C/3

X

LL O UJ

I I i I r I I I I I I I i I I I I I I I I I I 1 I I I ( 1 I I I I r I I I [ I I I I I I I I I I' I r I

1950 1960 1970 1980

YEAR

1990 2000 2010

Fig. 4.3: Yearly mean cosmic ray diurnal anisotropy phase (time of maximum) obtained using Neutron Monitor data at four stations, Oulu, Deep River, Climax and Huancayo. Solid vertical lines indicate the years of solar minimum and the periods between two-dashed hnes in each solar cycle indicate the epoch of solar polar field reversal.

s tate (A > O), phase shift to earlier hours s tar ts , reaches its minimum

value near solar minimum (in 1997) and then recovering to pre-reversal

level. These observations clearly indicate tha t the t ime of maximum is

influenced by the orientation of solar magnetic field ra the r t han by solar

activity and/or co rotating high-speed streams. The t ime of maximum

shows some rigidity dependence, as can be seen in Figure 4.3, (see also

Table-2), lowest value of phase (earliest time of maximum) of the diurnal

anisotropy is observed at Huancayo, with highest threshold rigidity

among all the four locations.

To provide the average perspective of the diurnal anisotropy, on

the scale of a solar cycle and over a polarity s tate of the Heliosphere, I

have plotted, in Figures 4.4 (a and b), the vector diagrams over harmonic

dial for complete solar cycles 19 (1955-1964), 20 (1966-1975), 21 (1976-

38

1985), 22 (1986-1996) and incomplete cycle 23 (1997-2003) as well as (in

Figures 4.5) for each A < 0 (1961-1970, 1981-1990) and A > 0 (1971-1980,

1991-1999) polarity epoch.

Although the amplitude of diurnal anisotropy displays a clear 11-

year sunspot cycle, when averaged over a complete cycle, no significant

and/or systematic difference in solar cycle averaged amplitudes from one

cycle to the other or between even and odd cycles is observed. Similarly

phase too, when averaged over a complete solar cycle, does not show any

significant and/or systematic shift from one cycle to the other or between

even and odd solar cycles. When averaged over a polarity state of the

heliospheric magnetic field (A < 0 & A > O), the amplitudes are nearly

same for both the polarity states. But the phase shift to earlier hours

during seventies and nineties (A > 0) is clearly evident even in the

average vectors (Figures 4.5, a and b).

Figures 4.6 shows the frequency distributions of the amplitude

of diurnal anisotropy for days of solar cycles 19, 20, 21, 22, and 23.

Amplitudes calculated for each day of a solar cycle and plotted in a

histogram, show almost similar distribution for all the cycles. Moreover,

the frequency distributions of the time of maximum for days of various

solar cycles, plotted in Figures 4.7, is also similar and no phase shift from

one solar cycle to other is seen in the average phase values.

In Figures 4.8 I have shown the frequency distribution of diurnal

amplitudes for days in different polarity states of the Heliosphere (A>0

and A<0). No significant difference in the amplitudes distribution is seen

in these histogram plots. However, the frequency distributions of the

time of maximum (Figures 4.9) clearly indicate the shifting of the diurnal

phase towards earlier hours during seventies (1971-1979) and nineties

(1991-1999). Thus frequency distribution plots with complete spectrum

shown in Figure 4.6, 4.7 and Figure 4.8, 4.9 complement the conclusions

drawn from average vector diagrams plotted in Figure 4.4 and 4.5

respectively.

39

00 h

HI Q

:D

_ i Q.

<

12 h

OOh

12h

06 h

06h

Fig. 4.4 a: Diurnal anisotropy vectors on a 24-hour harmonic dial averaged over complete solar activity cycles for stations Oulu and Deep River.

40

OOh

LU Q =3 H _l Q.

<

02

0.0

0,2

0.0

12h

OOh

12 h

06h

06 h

Fig. 4.4 b: Diurnal anisotropy vectors on a 24-hour harmonic dial averaged over complete solar activity cycles for stations Climax and Huancayo.

41

00 h

Q 3

Q.

<

0.2

12 h

OOh

06 h

06h

12h

Fig. 4.5 a: Diurnal anisotropy vectors on a 24-hour harmonic dial averaged over solar polarity epochs (A > 0 and A < 0), for stations Oulu and deep River.

42

OOh

0.2

06h

LU Q 3

Q.

<

0.0

12h

OOh

12 h

06 h

Fig. 4.5 b- Diurnal anisotropy vectors on a 24-hour harmonic dial averaged over solar polarity epochs (A > 0 and A < O), for s tat ions Climax and Huancayo.

43

20

I I 1 1 1

18

16 j i

14

i '2 1

'°! 1

8 •

6 j

4

2

-• 1

i

1 1 1 1

OULU 1965-75

i r-- .

TM-,.

. -

-

-

-

-

-

-

-

-

HUUl.,l o o o o o o o o o

AMPLITUDE (%) AMPLITUDE {%)

d b o d b o o o

20

? ' UJ

LU

tc cc ID 12 O o o u. 10 o >-" n Ui ID O „ UJ 6 a:

4

2

Q

n 1

• ~

- OULU

1997-2003

-

1

! .

-;

-•

o o o o

AMPLITUDE (%) AMPLITUDE (%)

Fig. 4.6 a'- Amplitude distribution of diurnal vectors for days of various solar cycles at station Oulu.

44

IT D O

O > O Z UJ

O

1 ' I • I ' I ' 1 ' 1 ' 1 ' I ' I

DEEP RIVER 1965-1975

_1_1_

O O O O O O O C J i ^ r -

o u o u_ o

a

20

i a . 1 ! ,

16 -

' i 12 -

1

-H °n 11

- i

i

1 DEEP RIVER 1976-1985

j , 1

,

', i

i

n 1 1

1 '

i 1 ! ^.

I ' I

-

-

-

-

-

-

-_

AMPLITUDE (%)

^ ifi A -i lA

AMPLITUDE (%)

3 o o o

§

r : l lT-T- t -^

nunun AMPLITUDE (%)

Fig. 4.6 b: Amplitude distribution of diurnal vectors for days of various solar cycles at station Deep River.

45

o

-T—!—1—1—1—r—1—I—r—I—I—I—r

CLIMAX 1954-64

• : !

1-1

c m U.i II-ir -> r -1

C)

o

22

20

(8

16

14

10

o

T — 1 — r — I — t — ; — 1 "

n

CLIMAX 1966-75

: I

AMPLITUDE (%)

rf. 6 ^ r

AMPLITUDE (%)

2 2 l ^ - T -

n O uj a:

CLIMAX 1976-85 £ 18

^ 16 l i i t r M ac d 12 o o 10

" « >-o 2 6 UJ

o •* Ol CC 2

0

-1—J—1— (— 1 p I I 1 1 1 1 1 1 -l 1- • 1 1

f ' CLIMAX 1986-96

' i ; 1 1 t

1 ' \

, 1 1 • 1 1 '

1

' 1 1

, !

" , 1 1

i—T

....,

^ ,1 . ...Orir-te-,,™-,™--.^

-•

--

-•

rS 4 -ri. ri C O O

AMPLITUDE (%} L. CJ o o — " '

AMPLITUDE {%)

20

t i s UJ

z ^^ m

B 12 O o 10

o Z 6

g 4 ^ 2

0

FT" 1—r ' > ) 1 ,_.,.,. . , ,. ., ,, ,. r

1 1

j 1 ! 1

1 1 1

• 1 1 • l „ ,

1 1 1

1 1 i 1 i

i!

lixi-IIil:.

CLIMAX 1997-2003

' --'

-

-

AMPLITUDE (%)

Fig. 4.6 c" Amplitude distribution of diurnal vectors for days of various solar cycles at station Climax.

46

' ' ' ' ' ' ' ' 20 1 1

' i i -

t ' 1 1 T' 1

HUANCAYO 1954-1965

'- i . ^^i '

12 i-1 '

10 p j

\" 1

I 1

el' 1

^ ^ i 2 -

' i 1

1 .1 ;

-; 1

1 1

1 , 1

1 tl+TI-n—i—

-

-

-

-

-

-

-

-

-

20

18

16

14

12

10

8

6

4

2

1

1

! i

- 1 •- I

1

! i 1

HUANCAYO 1965-1975

: i . 1

!

''

1

1

1 — 1 —

-

-

-

-

-

-

-

-

-

s ^ i AMPLITUDE (%) AMPLITUDE (%)

^r

HUANCAYO 1976-1985

O O O O O O O O O r ^ T -

20

18

^ 16

UJ

z " a: cr =) 12 o o o u_ 10

o >-Lll 3 LU 6 Q: LL

4

2

r~ " 1

1

• |

. 1 1

.1 1

"

-

HUANCAYO 1986-1996

-

•

-1

-1

1 1

1

1 : 1

1 ! • . ~h-v_,—,

»- CM I'l ^ tn (O t oi a> o I-o o o d o o d o o ' - ' -

AMPLITUDE (%) AMPLITUDE (%)

Fig. 4.6 d: Amplitude distribution of diurnal vectors for days of various solar cycles at station Huancayo.

47

TIME OF MAXIMUM (HRS.) TIME OF MAXIMUM (HRS )

O O

f? 4 -

- T — I — I — I — I — r -

OULU 1986-96

r

n r 1

11 (TTf

ih

1 'T in (O r~~ •:

TIME OF MAXIMUM (HRS.)

i S S S F

OULU 1997-2003

Xlilll f t -

J_L 1 ta I-

TIME OF MAXIMUM (HRS)

Fig. 4.7 a- Phase distribution of diurnal vectors for days of various solar cycles at station Oulu.

48

D O O o

DEEP RIVER 1965-1975

[THl J-X ,Etd PHASE (HOUR)

o o O

o

t "

-1—I—I—I—I—1—I—I—!—I—I—1—I—

DEEP RIVER 1976-1985

nxdl-

i

PHASE (HOUR)

!:tn:

D O

DEEP RIVER 1986-1996

''"f''"i"'"i"'"i' * I ' I ' * 'I""I'"'!'"'I'' I ' I M PHASE (HOUR)

Fig. 4.7 b: Phase distribution of diurnal vectors for days of various solar cycles at station Deep River.

49

— I — I — I — J — I — f — T "

CLIMAX 1954-64

HfflMCi

CLIMAX 1965-75

I ,

J ,

I i1 d) cfi ' - (N f^ *? lA '

PHASE (HOUR)

" cfi 6 ^ c o ^ lA «

PHASE (HOUR)

O O O

-

T

CLIMAX 1976-85

TRT

- 1 I -T 1 T i )—( i—r I -I—(

-

i j 1 j i

1 1

t£' .1

i : • '

ii l i f

lu 12 a a; 3 '»

CLIMAX 1986-96

tomsl ' i <

: 2 S 3 ;

PHASE (HOUR)

d) -^ (N (^ i i lA <ib (

PHASE (HOUR)

?, 10-

-1—r~t—I—r—I—I—I—I—r—T—r-

CUMAX 1997-2003

n :3xtcnfXLU JXtO

PHASE (HOUR)

Fig. 4.7 c: Phase distribution of diurnal vectors for days of various solar cycles at station Climax.

50

o o o

HUANCAYO 1954-1964

r • ' • ' I ' I ' 'f ' '"i ^ I 'T

) O •- Ol m TT j ^ (O '^ i

PHASE (HOUR)

o

o >-o z

^ <

HUANCAYO 1965-1975

r i 1 1

I !• I I

I ' - K i r t ' i ' u ' j t i i ' l c i i T ' T T

PHASE (HOUR)

I " I • ' I •'•'!"

CC

o o o o >-o z

HUANCAYO 1976-1985

n o i .

r

r 1

m , „ , . „ . . ) O T- (N to •

) d) d T^ CN r • " - CM tN Nl f

PHASE (HOUR)

O O O

3

o

HUANCAYO 1986-1996

r" • ' ' r ! 7 CN <^ <f uj n> h

I I [—I * I ' I

S S !

PHASE (HOUR)

Fig. 4.7 d: Phase distribution of diurnal vectors for days of various solar cycles at station Huancayo.

51

S i 16 LU

o a: a:

o o u. 10

o

3

o

~T I 1—I—I—T"

OULU 1961-70

Idi o d d d o d o ' o d ' ^ ' - ' T -

in (O r- oo oi

^ u") (D r i CO

AMPLITUDE (%)

Si 16 LU O g 14

3 ^ o £ 10 o > O 8

z LU 3

6 LU

~\ I ! I I—1 1 T"

a

OULU 1971-80

1— ( S f O ^ m t D r ^ o o C T O i - C N M ' V t D t D f ^ e o o ) d d d d d c > d d d ^ ^ T ^ » 7 » 7 ' 7 - ^ V ' 7 - ^ d i - t N r o T i - i o u l i t - ^ c o d d T ^

d d o d d d o d d ' < - ^ ' < - ^ TT LO (O r-- CO

AMPLITUDE (%)

>-o z LU

O

-1—I—I—I—I—I—1—1—I—I—I—I—I—r

OULU 1981-90

" - f s l f O ' ^ i O c p h - c o o i O ' - t N c o ^ m t D r - o o o i d d d d d d d d d ' - ^ ' - ' ' - ^ ' - ^ T - ' i - ^ T - ; . r ^ - ^ ' - r -

22

20

en O o o

>-o z LU 3 a

1 1 1 1 1 1 1 1 1 1 -T—r

• h

1 1 1 1 I I r

OULU 1991-2003

:

~1

' - ( N r o ' v i n ( £ ) r - - ( o o j O ' ~ r - i c o T r m < D d d d d d d d d d ' r ^ ' - T - - ^ ' - ^ ' ^ T -O T ^ r N i c o - ^ u i t p r ^ c o d d r ^ f s i i r i T r i n

d d d d d d o d d ' - ^ ' - - ^ ^ ^ ' -

AMPLITUDE (%) AMPLITUDE (%)

Fig. 4.8 a- Frequency distribution of diurnal amplitude on the days in different polarity epochs (A > 0 and A < O) of the heliospheric magnetic field at station Oulu.

52

a. X a o o

3

a

20

)S

16

14

i: 1 \

1, 1

•

.

' 1

1

1

1

1 : 1

' 1

1 1 i_...

' ' 1

1

1

' ' DEEP RIVER

1961-1970

"!

1

1 i

i 1

1 1 1

... _.!.,

- 1

1 I- 1 1

-

-

-

-

.

_

C3 O d o o o cfi "- (^ (J) 4 uS CO '

ai o r-

AMPLITUDE (%)

o o O

' I • I • ) • I • I I I • I • I I

Ll ,

I • ) • 1 1 1 ' 1 1 1 1

D E E P R IVER

197M980

r-u-^ o c p o d d d d o o T - ^ T - ^

o d c i c i c i d o o o T - i - ^

AMPLITUDE (%)

20

. 6 r ' , 1

S' 16 L - 1 1 UJ

Z 1 4 -

8 1 s ° LU

a. 4

2

r

"1

DEEP RIVER 1981-1990

-

~i 1

-

" 1

"1

! rh—v->™

-

-

"

-•

--

0 0 0 0 0 0 0 0 0 1 -

O O

o

?n

18

16

14

12

10

8

6

4

2

.

•

" r i

" 1

• 1

-1 • 1

1

• i

1

) • I " 1 ' 1 ' 1

'—1

! 1 ^

"( 1

1 1 ! 1 ~1

1

1 , 1

1

1

ihr-r

DEEP RIVER 1991-2003

•

_

' -

-

-

--

--

O O G O O O O

O O O

AMPLITUDE (%) AMPLITUDE (%)

Fig. 4.8 b- Frequency distribution of diurnal amplitude on the days in different polarity epochs (A > 0 and A < 0) of the heliospheric magnetic field at station Deep River.

53

20

--s;::, is

O 16

LU a: 14 Q;

7i .2 o O 10 u-^ a

>~ u Z 6 LU => ^ O " LU Cd 2

' ' -I—T'' r 1 1

1

• I 1 ,

1

~_

1 1 I

CUMAX 1951-60

. —

1

1 1

1

1

! 1 •- '^^^V-r^-^-,

T 1

-.

-.

--

•

9 9 9 ?

AMPLITUDE (%)

20

LU O 16 Z UJ Q: H a. H 12 O O 10 u. <-> « >-O Z 6 LU D , a " Lii

0

[ ^ . \"

-1 - 1

-

-T— - T - ~r- T r' 1" 1 1 1 1

1

'. I rrv-,

1 1 1

CLIMAX 1971-80

1 1

-. .

---

0 9 0 0 1 ^

d d o o d ^ " - ^

AMPLITUDE (%)

22

20

g 18 lU O 16

LU K 14

3 1 o O 10

o „

a

I ! -

I !

J L

20 L

£ 1 8 r 1

0 16 • Z

i r 14 -Q^ 1

5 - , 0 ' 0 10. ' ^ 1

0 8 '

> ; 0 1 Z 6 - , LU l ^ ^ L o "h LU I

° zt ot ! .

1

1

1

1 1 1

CLIMAX 1961-70

' 1 1 !

1 • -

1

1

'

1 1 1 1

1 I" I '. 1 i 1 nrrr-.--^

1

-

-_

-

HUUi AMPLITUDE (%)

3 O

20

18

14

12

10

8

6

4

2

- . CLIMAX 1981-90

' _

1

• 1

1

1

' 1

1

1 1

"1 1

1

r

1 1 1

1 1

! 1 " " . ^ - T — i — , . , - ™ , ^

-

' -------

5 2 3 3 3 3 3 d d d o d o

AMPLITUDE (%)

CUMAX 1991-2003

AMPLITUDE (%)

Fig. 4.8 c: Frequency distribution of diurnal amplitude on the days in different polarity epochs (A > 0 and A < O) of the heliospheric magnetic field at station Climax.

54

20

16

14

12

10

8

6

4

2

• • T ' •

' _|_ —r- ' '

~1

- !

- 1

1

- 1

i 1

r -

l _ ^

r - 1 1 1 • I

HUANCAYO 1951-1960

' '. "

1 1

"!

1

-

1- -

1

r-r-i_^ CN n ^ if) <o t 9 9 9 9 9 ' o o d o o d o o o

AMPLITUDE (%)

HUANCAYO 1961-1970

c j ) q ) 9 9 ^ 9 9 V ' d o o d d o o d '

AMPLITUDE (%)

20

in

16

14

12

10

8

6

4

2

1 1

1 ,

1 1

-

-

•

i HUANCAYO 1971-1980

-

1 '

1 1

-

-

"!

a_ o o q> OT o Q o 1^ o 1-

O O O O O O O G O

T — I — I — I — r -

r HUANCAYO 1981-1990

' I

AMPLITUDE (%) AMPLITUDE (%)

Fig. 4.8 d: Frequency distribution of diurnal amplitude on the days in different polarity epochs (A > 0 and A < 0) of the heliospheric magnetic field at station Huancayo.

55 ->"V- . hV

'•n n . i v C ^

a: a. z> o o o u. O > o

a a:

I I I I I I ! I I I I

OULU 1971-80

r

ohrfTrf y CTJO'i—cNtO'j'ixiifjr^-roCTJCj'—c

TIME OF MAXIMUM (HRS.) TIME OF MAXIMUM (HRS.)

O 12

a: a: z> a o O

O > o

a UJ

n I I I I I r" I I I I I I I I I

OULU 1991-2003

tftQ Id TIME OF MAXIMUM (HRS.)

- o o o i O ' - c N r o ^ i j

( J i O T - r > j f O " « i O ( o r

TIME OF MAXIMUM (HRS.)

Fig. 4.9 a: Frequency distribution of diurnal phase on the days in different polarity epochs (A > 0 and A < 0) of the heliospheric magnetic field at station Oulu.

56

O o o

DEEP RIVER 1961-1970

.i.u^.a

i !

..MJ

PHASE (HOUR)

~i—1—I—1—I—r

DEEP RIVER 1971-1980

, I

Illll tnttl 5 ^ ^ 3 '

PHASE (HOUR)

o o o

o

DEEP RIVER 1981-1990

imd

1

r ' I •••r*T' ' ' t " ' '

' - ( N f O ' j i n t o N - o p a i O T - c

M < D I ~ - c O O i O ' - C N r O '

PHASE (HOUR)

3 O o o

o

DEEP RIVER 1991-2003

1 5 2 3 3 4 S I

PHASE (HOUR)

Fig. 4.9 b- Frequency distribution of diurnal phase on the days in different polarity epochs (A > 0 and A < O) of the heliospheric magnetic field at station Deep River.

57

^ 2

CLIMAX 1951-60

IteMll Wn

PHASE (HOUR)

—I—\—1—1—1—r-

CLIMAX 1971-80

:TOxan. 11

''M. PHASE (HOUR)

CLIMAX 1961-70

cc 2-

IrTTTTT-TT m r^ ^ u i tp r^ C9 t

PHA'SE (HOUR)'

CLIMAX 1981-90

n

I^^TT^" y PHASE (HOUR)

O

>

"- 2

CLIMAX 1991-2003

TWfTfl inji PHASE (HOUR)

: s 8 E; !

Fig. 4.9 c: Frequency distribution of diurnal phase on the days in different polarity epochs (A > 0 and A < O) of the heliospheric magnetic field at station Climax.

58

cr D o o o

3 o ^ 4-u- '

HUANCAYO 1951-1960

, I

I

PHASE (HOUR)

HUANCAYO 1961-1970

PHASE (HOUR)

UJ O 12 z UJ

en 10-

o o o

o > o z LU D

o

HUANCAYO 1981-1990

affl PHASE (HOUR) PHASE (HOUR)

Fig. 4.9 d Frequency distribution of diurnal phase on the days in different polarity epochs (A > 0 and A < 0) of the heliospheric magnetic field at station Huancayo.

59

4.5 Discussion

In model calculations (see chapter 3 for details and references)

including drift effects, cosmic ray trajectories were calculated for the two

IMF configurations corresponding to two orientations of Sun's polar

magnetic field. During 1960s and 1980s (for example), when the IMF was

inward (A < O) above the heliospheric current sheet, galactic cosmic rays

enter the Heliosphere mainly in the ecliptic plane. During the 1970s and

1990s when the IMF was outward above the current sheet (A > O), cosmic

ray particles penetrate the Heliosphere more easily from polar regions.

During 1960 and 1980 (A < O), the convection diffusion model adequately

describes the solar diurnal variation because the cosmic rays entering

the Heliosphere diffuse predominantly in the ecliptic plane, with the net

inflow in the ecliptic plane balancing the net outflow in the ecliptic plane

(the convective component), leading to an azimuthal cosmic ray diurnal

variation. During the 1970s and 1990s (A > 0), with cosmic rays entering

preferentially by way of the poles, there is a reduction in the inward

diffusive component in the ecliptic plane, leading to a net diurnal

variation that has its maximum at an earlier time. In this case the net

inflow of cosmic rays from the poles balances the net outflow in the

ecliptic plane, with a relative increase of the radial component of the

diurnal variation, and a shift in phase to earlier hours.

4.6 Conclusions

In this work, the cosmic ray diurnal anisotropy using data

over a period of about 50 years from four neutron monitors has been

determined. Following conclusions can be drawn from this study.

The amplitude of the cosmic ray diurnal anisotropy varies

with a period of one solar activity cycle (~ 11-years), while the phase of

the diurnal anisotropy varies with a period of one solar magnetic cycle (~

22-years) i.e. two solar cycles.

In each solar activity cycle, the amplitude is observed to be

enhanced for one/two years during declining phase when co-rotating

high-speed streams from coronal holes are prevalent.

60

Amplitude is influenced by solar activity and co rotating high

speed solar wind streams while the time of maximum is influenced by

the orientation of solar magnetic field,' the shift in phase appears to be

related to switch of the Heliosphere from one magnetic state to another

following polar field reversal and the consequent change in preferential

entry of cosmic ray particles into the Heliosphere.

The amplitude of diurnal anisotropy is independent of the

threshold rigidity of the cosmic ray particles. However, the time of

maximum depends upon the threshold rigidity of the observing station.

Time of maximum of the diurnal anisotropy is dependent on

the polarity state of the Heliosphere; it is influenced by the orientation of

the solar magnetic field rather than by solar activity and/or co rotating

high-speed solar wind streams. The phase shift to earlier hours in each

solar magnetic cycle starts after the solar polarity reverses from negative

(A < 0) to positive state (A > 0).

The solar cycle averaged diurnal amplitude is almost same for

different solar cycles and no significant change is observed from one cycle

to the other or between odd and even cycles. The average time of

maximum too does not change from one cycle to the other when averaged

over a solar activity cycle. However, the average phase during one

polarity state of the Heliosphere (e.g. A > O) is significantly different from

the other polarity state (A < O) and it is shifted to earlier hours during A

< 0 state as compared to A > 0 state.

61

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/« t

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